An Easter Egg can be modelled in polar coordinates as: r=\frac{16}{5-3 \sin \theta} b) Hence or otherwise sketch the ellipse indicating all intercepts with the axes and showing all working.

[4 marks] \text { a) Convert this into the standard form for an ellipse in terms of } x \text { and } y \cdot \frac{\left(x-x_{c}\right)^{2}}{a^{2}}+\frac{\left(y-y_{c}\right)^{2}}{b^{2}}=1[4 \text { marks }]